(3a+1)(5a-7)=

Solution for (3a+1)(5a-7)= equation:

(3a+1)(5a-7)=

We move all terms to the left:

(3a+1)(5a-7)-()=0

We add all the numbers together, and all the variables

(3a+1)(5a-7)=0

We multiply parentheses ..

(+15a^2-21a+5a-7)=0

We get rid of parentheses

15a^2-21a+5a-7=0

We add all the numbers together, and all the variables

15a^2-16a-7=0

a = 15; b = -16; c = -7;
Δ = b2-4ac
Δ = -162-4·15·(-7)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-26}{2*15}=\frac{-10}{30}
=-1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+26}{2*15}=\frac{42}{30}
=1+2/5
$